Explanation Show the P − v diagram of an Otto cycle. Figure-(1) Write the expression for compression ratio. r = V 1 V 2 (I) Here, the compression ratio is r , the initial volume is V 1 and volume at point 2 is V 2 . Write the equations for isentropic compression and isentropic expansion. T 2 = T 1 r k − 1 (II) Here, the final temperature is T 2 , initial temperature is T 1 and specific heat ratio is k . Write the expression for the temperature at point 4. T 4 = T 3 ( 1 r ) k − 1 (III) Here, the temperature at point 4 is T 4 and temperature at point 3 is T 3 . Write the expression for first law of thermodynamics. w n e t = c v ( T 3 − T 4 ) − c v ( T 2 − T 1 ) (IV) Here, the net work done is w n e t and specific heat at constant volume is c v . Write the expression for the initial volume. V 1 = R T 1 P 1 (V) Here, the gas constant is R and pressure at point 1 is P 1 . Write the expression for the total mass of air for cylinders. m = N c y l π B 2 S / 4 V 1 (VI) Now the total work generated per cycle is, W n e t = m w n e t (VII) Here, the total work done is W n e t . Write the expression for the power. W ˙ n e t = W n e t n ˙ N r e v (VIII) Here, the power is W ˙ n e t , the revolutions is n ˙ and number of cycle is N r e v . Conclusion: Substitute 0.098 V 1 for V 2 in Equation (I). r = V 1 0.098 V 1 = 10.20 Substitute 10.20 for, 565 R for T 1 and 1.4 for k in Equation (II). T 2 = ( 565 R ) ( 10.20 ) 1.4 − 1 = ( 565 R ) ( 2.53 ) = 1429.45 R Substitute 2860 R for T 3 , 10.20 for r and 1.4 for k in Equation (III). T 4 = ( 2860 R ) ( 1 10.20 ) 1.4 − 1 = ( 2860 R ) ( 0.394 ) = 1126.84 R Substitute 0.171 Btu/lbm .R for c v , 1126.84 R for T 4 , 1429.45 R for T 2 , 565 R for T 1 and 2860 R for T 3 in Equation (IV)

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ISBN: 8220102809444

Author: CENGEL

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Chapter 9.12, Problem 36P

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The power generated by an engine that is operated on ideal Otto cycle

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Chapter 9.12, Problem 35P

Chapter 9.12, Problem 37P

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